P
US12427707B2ActiveUtilityPatentIndex 40

Twin-screw extrusion device and processing method therefor

Assignee: UNIV WUYIPriority: Feb 4, 2024Filed: Mar 21, 2024Granted: Sep 30, 2025
Est. expiryFeb 4, 2044(~17.6 yrs left)· nominal 20-yr term from priority
Inventors:XU BAIPINGYU HUIWENTan LingcaoXIAO SHUPINGHUANG JIARONGXU WENHUA
B29C 48/2526B29C 48/64B29C 48/59B29C 48/40B29C 48/832B29C 48/802B29C 48/405B29C 48/402
40
PatentIndex Score
0
Cited by
5
References
6
Claims

Abstract

A twin-screw extrusion device is disclosed, which includes a barrel and a twin-screw mechanism, the twin-screw mechanism includes a first screw, a second screw and a drive assembly, the drive assembly includes a plurality of idler gears and two mutually engaged elliptical gears, one of the elliptical gears is fixedly connected to the first screw, the other elliptical gear synchronously rotates with one of the idler gears, the last idler gear is fixedly connected to the second screw, a rotation speed of the first screw is ω 1 =N, an eccentricity of each of the elliptical gears is k, 0<k<0.8, an included angle between a connecting line of the first screw and the second screw and a long axis of each of the elliptical gears is φ, and a rotation speed of the second screw is ω 2 , satisfying ω 2 = ( 1 - k 2 ) ⁢ N 1 - 2 ⁢ k ⁢ cos ⁢ φ + k 2 .

Claims

exact text as granted — not AI-modified
What is claimed is: 
     
       1. A twin-screw extrusion device, comprising:
 a barrel; 
 a twin-screw mechanism comprising a first screw, a second screw and a drive assembly, wherein the first screw and the second screw are both rotatably connected to the barrel, the first screw is engaged with the second screw, the drive assembly comprises a plurality of idler gears and two mutually engaged elliptical gears, one of the elliptical gears is fixedly connected to the first screw, the other elliptical gear is synchronously rotatable with one of the idler gears, the plurality of idler gears are in transmission connection, and a last one of the idler gears is fixedly connected to the second screw, so that the first screw and the second screw are rotatable in a same direction;
 wherein the first screw is rotatable at a constant speed, a rotation speed of the first screw is ω 1 =N, an eccentricity of each of the elliptical gears is k, 0<k<0.8, an included angle between a connecting line of the first screw and the second screw and a long axis of each of the elliptical gears is φ, and a rotation speed of the second screw is ω 2 , satisfying 
 
 
       
         
           
             
               
                 ω 
                 2 
               
               = 
               
                 
                   
                     
                       ( 
                       
                         1 
                         - 
                         
                           k 
                           2 
                         
                       
                       ) 
                     
                     ⁢ 
                     N 
                   
                   
                     1 
                     - 
                     
                       2 
                       ⁢ 
                       
                         k 
                         ⁢ 
                         cos 
                       
                       ⁢ 
                       φ 
                     
                     + 
                     
                       k 
                       2 
                     
                   
                 
                 . 
               
             
           
         
       
     
     
       2. The twin-screw extrusion device according to  claim 1 , wherein an outer diameter of the first screw and the second screw is D, an outer radius of the first screw and the second screw is R, an inner diameter of the first screw and the second screw is d, and an inner radius of the first screw and the second screw is r;
 a center distance between the first screw and the second screw is C, and 
 
       
         
           
             
               
                 C 
                 = 
                 
                   
                     R 
                     + 
                     r 
                   
                   = 
                   
                     
                       ( 
                       
                         D 
                         + 
                         d 
                       
                       ) 
                     
                     2 
                   
                 
               
               ; 
             
           
         
         an engaged angle of the first screw and the second screw is β, and 
       
       
         
           
             
               
                 β 
                 = 
                 
                   arccos 
                   ⁢ 
                      
                   
                     ( 
                     
                       C 
                       D 
                     
                     ) 
                   
                 
               
               ; 
             
           
         
         a section of the first screw is formed by connecting curve arcs S 12 , S 23 , S 34 , S 45 , S 56 , S 67 , S 78 , S 89  and S 91 , and corresponding central angles are φ 1 , φ 2 +β, φ 3 , φ 4 +β, φ 5 , φ 6 +β, φ 7 , φ 8 +β and φ 9 ; a section of the second screw is formed by S′ 12 , S′ 23 , S′ 34 , S′ 45 , S′ 56 , S′ 67 , S′ 78 , S′ 89  and S′ 91 , corresponding central angels are φ′ 1 , φ′ 2 +β, φ′ 3 , φ′ 4 +β, φ′ 5 , φ 6 +β, φ′ 7 , φ′ 8 +β and φ′ 9 , a rotation center of the first screw is O, and a rotation center of the second screw is O′; 
         S 12 , S 56  and S 91  are a root circle arc with O as a circle center and r as a radius; S 34  and S 78  are a top circle arc with O as a circle center and r as a radius; S′ 12 , S′ 56  and S′ 91  are a top circle arc with O′ as a circle center and R as a radius; S′ 34  and S′ 78  are a root circle arc with O′ as a circle center and r as a radius; 
         an initial phase angle is θ 0 , 0≤θ 0 ≤360°, and K d =(1+k)/(1−k); 
         the central angels satisfy: 
       
       
         
           
             
               
                 
                   φ 
                   1 
                   ′ 
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   φ 
                                   1 
                                 
                                 ⁢ 
                                 − 
                                 ⁢ 
                                 
                                   θ 
                                   0 
                                 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                           ⁡ 
                             
                           
                             ( 
                             
                               
                                 θ 
                                 0 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     φ 
                     1 
                     ′ 
                   
                   + 
                   β 
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                           ⁡ 
                              
                           
                             ( 
                             
                               
                                 
                                   φ 
                                   1 
                                 
                                 + 
                                 
                                   φ 
                                   2 
                                 
                                 ⁢ 
                                 − 
                                 ⁢ 
                                 
                                   θ 
                                   0 
                                 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 θ 
                                 0 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     φ 
                     1 
                     ′ 
                   
                   + 
                   β 
                   + 
                   
                     φ 
                     2 
                     ′ 
                   
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   φ 
                                   1 
                                 
                                 + 
                                 
                                   φ 
                                   2 
                                 
                                 + 
                                 β 
                                 ⁢ 
                                 − 
                                 ⁢ 
                                 
                                   θ 
                                   0 
                                 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 θ 
                                 0 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     φ 
                     1 
                     ′ 
                   
                   + 
                   β 
                   + 
                   
                     φ 
                     2 
                     ′ 
                   
                   + 
                   
                     φ 
                     3 
                     ′ 
                   
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   φ 
                                   1 
                                 
                                 + 
                                 
                                   φ 
                                   2 
                                 
                                 + 
                                 β 
                                 + 
                                 
                                   φ 
                                   3 
                                 
                                 ⁢ 
                                 − 
                                 ⁢ 
                                 
                                   θ 
                                   0 
                                 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 θ 
                                 0 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     φ 
                     1 
                     ′ 
                   
                   + 
                   β 
                   + 
                   
                     φ 
                     2 
                     ′ 
                   
                   + 
                   
                     φ 
                     3 
                     ′ 
                   
                   + 
                   
                     φ 
                     4 
                     ′ 
                   
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   φ 
                                   1 
                                 
                                 + 
                                 
                                   φ 
                                   2 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   β 
                                 
                                 + 
                                 
                                   φ 
                                   3 
                                 
                                 ⁢ 
                                 − 
                                 ⁢ 
                                 
                                   θ 
                                   0 
                                 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 θ 
                                 0 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     φ 
                     1 
                     ′ 
                   
                   + 
                   
                     2 
                     ⁢ 
                     β 
                   
                   + 
                   
                     φ 
                     2 
                     ′ 
                   
                   + 
                   
                     φ 
                     3 
                     ′ 
                   
                   + 
                   
                     φ 
                     4 
                     ′ 
                   
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   φ 
                                   1 
                                 
                                 + 
                                 
                                   φ 
                                   2 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   β 
                                 
                                 + 
                                 
                                   φ 
                                   3 
                                 
                                 + 
                                 
                                   φ 
                                   4 
                                 
                                 ⁢ 
                                 − 
                                 ⁢ 
                                 
                                   θ 
                                   0 
                                 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 θ 
                                 0 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     φ 
                     1 
                     ′ 
                   
                   + 
                   
                     2 
                     ⁢ 
                     β 
                   
                   + 
                   
                     φ 
                     2 
                     ′ 
                   
                   + 
                   
                     φ 
                     3 
                     ′ 
                   
                   + 
                   
                     φ 
                     4 
                     ′ 
                   
                   + 
                   
                     φ 
                     5 
                     ′ 
                   
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                             
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   φ 
                                   1 
                                 
                                 + 
                                 
                                   φ 
                                   2 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   β 
                                 
                                 + 
                                 
                                   φ 
                                   3 
                                 
                                 + 
                                 
                                   φ 
                                   4 
                                 
                                 + 
                                 
                                   φ 
                                   5 
                                 
                                 ⁢ 
                                 − 
                                 ⁢ 
                                 
                                   θ 
                                   0 
                                 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 θ 
                                 0 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     φ 
                     1 
                     ′ 
                   
                   + 
                   
                     3 
                     ⁢ 
                     β 
                   
                   + 
                   
                     φ 
                     2 
                     ′ 
                   
                   + 
                   
                     φ 
                     3 
                     ′ 
                   
                   + 
                   
                     φ 
                     4 
                     ′ 
                   
                   + 
                   
                     φ 
                     5 
                     ′ 
                   
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   φ 
                                   1 
                                 
                                 + 
                                 
                                   φ 
                                   2 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   β 
                                 
                                 + 
                                 
                                   φ 
                                   3 
                                 
                                 + 
                                 
                                   φ 
                                   4 
                                 
                                 + 
                                 
                                   φ 
                                   5 
                                 
                                 + 
                                 
                                   φ 
                                   6 
                                 
                                 ⁢ 
                                 − 
                                 ⁢ 
                                 
                                   θ 
                                   0 
                                 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 θ 
                                 0 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     φ 
                     1 
                     ′ 
                   
                   + 
                   
                     3 
                     ⁢ 
                     β 
                   
                   + 
                   
                     φ 
                     2 
                     ′ 
                   
                   + 
                   
                     φ 
                     3 
                     ′ 
                   
                   + 
                   
                     φ 
                     4 
                     ′ 
                   
                   + 
                   
                     φ 
                     5 
                     ′ 
                   
                   + 
                   
                     φ 
                     6 
                     ′ 
                   
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   φ 
                                   1 
                                 
                                 + 
                                 
                                   φ 
                                   2 
                                 
                                 + 
                                 
                                   3 
                                   ⁢ 
                                   β 
                                 
                                 + 
                                 
                                   φ 
                                   3 
                                 
                                 + 
                                 
                                   φ 
                                   4 
                                 
                                 + 
                                 
                                   φ 
                                   5 
                                 
                                 + 
                                 
                                   φ 
                                   6 
                                 
                                 ⁢ 
                                 − 
                                 ⁢ 
                                 
                                   θ 
                                   0 
                                 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 θ 
                                 0 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     φ 
                     1 
                     ′ 
                   
                   + 
                   
                     3 
                     ⁢ 
                     β 
                   
                   + 
                   
                     φ 
                     2 
                     ′ 
                   
                   + 
                   
                     φ 
                     3 
                     ′ 
                   
                   + 
                   
                     φ 
                     4 
                     ′ 
                   
                   + 
                   
                     φ 
                     5 
                     ′ 
                   
                   + 
                   
                     φ 
                     6 
                     ′ 
                   
                   + 
                   
                     φ 
                     7 
                     ′ 
                   
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   φ 
                                   1 
                                 
                                 + 
                                 
                                   φ 
                                   2 
                                 
                                 + 
                                 
                                   3 
                                   ⁢ 
                                   β 
                                 
                                 + 
                                 
                                   φ 
                                   3 
                                 
                                 + 
                                 
                                   φ 
                                   4 
                                 
                                 + 
                                 
                                   φ 
                                   5 
                                 
                                 + 
                                 
                                   φ 
                                   6 
                                 
                                 + 
                                 
                                   φ 
                                   7 
                                 
                                 ⁢ 
                                 − 
                                 ⁢ 
                                 
                                   θ 
                                   0 
                                 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 θ 
                                 0 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     φ 
                     1 
                     ′ 
                   
                   + 
                   
                     3 
                     ⁢ 
                     β 
                   
                   + 
                   
                     φ 
                     2 
                     ′ 
                   
                   + 
                   
                     φ 
                     3 
                     ′ 
                   
                   + 
                   
                     φ 
                     4 
                     ′ 
                   
                   + 
                   
                     φ 
                     5 
                     ′ 
                   
                   + 
                   
                     φ 
                     6 
                     ′ 
                   
                   + 
                   
                     φ 
                     7 
                     ′ 
                   
                   + 
                   
                     φ 
                     8 
                     ′ 
                   
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   φ 
                                   1 
                                 
                                 + 
                                 
                                   φ 
                                   2 
                                 
                                 + 
                                 
                                   4 
                                   ⁢ 
                                   β 
                                 
                                 + 
                                 
                                   φ 
                                   3 
                                 
                                 + 
                                 
                                   φ 
                                   4 
                                 
                                 + 
                                 
                                   φ 
                                   5 
                                 
                                 + 
                                 
                                   φ 
                                   6 
                                 
                                 + 
                                 
                                   φ 
                                   7 
                                 
                                 ⁢ 
                                 − 
                                 ⁢ 
                                 
                                   θ 
                                   0 
                                 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 θ 
                                 0 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     φ 
                     1 
                     ′ 
                   
                   + 
                   
                     4 
                     ⁢ 
                     β 
                   
                   + 
                   
                     φ 
                     2 
                     ′ 
                   
                   + 
                   
                     φ 
                     3 
                     ′ 
                   
                   + 
                   
                     φ 
                     4 
                     ′ 
                   
                   + 
                   
                     φ 
                     5 
                     ′ 
                   
                   + 
                   
                     φ 
                     6 
                     ′ 
                   
                   + 
                   
                     φ 
                     7 
                     ′ 
                   
                   + 
                   
                     φ 
                     8 
                     ′ 
                   
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   φ 
                                   1 
                                 
                                 + 
                                 
                                   φ 
                                   2 
                                 
                                 + 
                                 
                                   4 
                                   ⁢ 
                                   β 
                                 
                                 + 
                                 
                                   φ 
                                   3 
                                 
                                 + 
                                 
                                   φ 
                                   4 
                                 
                                 + 
                                 
                                   φ 
                                   5 
                                 
                                 + 
                                 
                                   φ 
                                   6 
                                 
                                 + 
                                 
                                   φ 
                                   7 
                                 
                                 + 
                                 
                                   φ 
                                   8 
                                 
                                 ⁢ 
                                 − 
                                 ⁢ 
                                 
                                   θ 
                                   0 
                                 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 θ 
                                 0 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     φ 
                     1 
                     ′ 
                   
                   + 
                   
                     4 
                     ⁢ 
                     β 
                   
                   + 
                   
                     φ 
                     2 
                     ′ 
                   
                   + 
                   
                     φ 
                     3 
                     ′ 
                   
                   + 
                   
                     φ 
                     4 
                     ′ 
                   
                   + 
                   
                     φ 
                     5 
                     ′ 
                   
                   + 
                   
                     φ 
                     6 
                     ′ 
                   
                   + 
                   
                     φ 
                     7 
                     ′ 
                   
                   + 
                   
                     φ 
                     8 
                     ′ 
                   
                   + 
                   
                     φ 
                     9 
                     ′ 
                   
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   φ 
                                   1 
                                 
                                 + 
                                 
                                   φ 
                                   2 
                                 
                                 + 
                                 
                                   4 
                                   ⁢ 
                                   β 
                                 
                                 + 
                                 
                                   φ 
                                   3 
                                 
                                 + 
                                 
                                   φ 
                                   4 
                                 
                                 + 
                                 
                                   φ 
                                   5 
                                 
                                 + 
                                 
                                   φ 
                                   6 
                                 
                                 + 
                                 
                                   φ 
                                   7 
                                 
                                 + 
                                 
                                   φ 
                                   8 
                                 
                                 + 
                                 
                                   φ 
                                   9 
                                 
                                 ⁢ 
                                 − 
                                 ⁢ 
                                 
                                   θ 
                                   0 
                                 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         
                           tan 
                              
                           ⁡ 
                           
                             ( 
                             
                               
                                 θ 
                                 0 
                               
                               2 
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     
                       
                         ∑ 
                           
                       
                       
                         i 
                         = 
                         1 
                       
                       9 
                     
                     ⁢ 
                     
                       φ 
                       i 
                     
                   
                   + 
                   
                     4 
                     ⁢ 
                     β 
                   
                 
                 = 
                 360 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     
                       ∑ 
                         
                     
                     
                       i 
                       = 
                       1 
                     
                     9 
                   
                   ⁢ 
                   
                     φ 
                     1 
                     ′ 
                   
                 
                 + 
                 
                   4 
                   ⁢ 
                   β 
                 
               
               = 
               360. 
             
           
         
       
     
     
       3. The twin-screw extrusion device according to  claim 2 , wherein connection points between every two adjacent curve arcs of the first screw is M 1 , M 2 , M 3 , M 4 , M 5 , M 6 , M 7 , M 8  and M 9 , which respectively correspond to curve arcs S 12 , S 23 , S 34 , S 45 , S 56 , S 67 , S 78 , S 89  and S 91 , and an auxiliary angle is given as θ, 0≤θ≤β;
 OM 2  is taken as a polar axis, a polar diameter corresponding to any position of the curve arc S 23  is OP 2 =ρ 2 (θ), and an included angle between the polar diameter OP 2  and the polar axis OM 2  is a polar angle ε 2 (θ), which satisfies: 
 
       
         
           
             
               
                 
                   
                     ε 
                     2 
                   
                   ( 
                   θ 
                   ) 
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     
                       arctan 
                          
                       [ 
                       
                         tan 
                         ⁢ 
                            
                         
                           ( 
                           
                             
                               
                                 
                                   φ 
                                   1 
                                   ′ 
                                 
                                 + 
                                 θ 
                               
                               2 
                             
                             - 
                             
                               a 
                               ⁢ 
                               tan 
                               ⁢ 
                                  
                               
                                 ( 
                                 
                                   
                                     K 
                                     d 
                                   
                                   ⁢ 
                                   tan 
                                   ⁢ 
                                      
                                   
                                     ( 
                                     
                                       
                                         θ 
                                         0 
                                       
                                       2 
                                     
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                           ) 
                         
                         / 
                         
                           K 
                           d 
                         
                       
                       ] 
                     
                   
                   + 
                   
                     θ 
                     0 
                   
                   - 
                   
                     φ 
                     1 
                   
                   + 
                   
                     
                       arctan 
                     
                     ⁢ 
                     
                          
                     
                     
                       ( 
                       
                         
                           R 
                           ⁢ 
                              
                           sin 
                           ⁢ 
                           θ 
                         
                         
                           C 
                           - 
                           
                             R 
                             ⁢ 
                                
                             cos 
                             ⁢ 
                             θ 
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     ρ 
                     2 
                   
                   ( 
                   θ 
                   ) 
                 
                 = 
                 
                   
                     
                       C 
                       2 
                     
                     + 
                     
                       R 
                       2 
                     
                     - 
                     
                       2 
                       ⁢ 
                       CR 
                       ⁢ 
                          
                       cos 
                       ⁢ 
                       θ 
                     
                   
                 
               
               ; 
             
           
         
         OM 5  is taken as a polar axis, a polar diameter corresponding to any position of the curve arc S 45  is OP 5 =ρ 4 (θ), and an included angle between the polar diameter OP 5  and the polar axis OM 5  is a polar angle ε 4 (θ), which satisfies: 
       
       
         
           
             
               
                 
                   
                     ε 
                     4 
                   
                   ( 
                   θ 
                   ) 
                 
                 = 
                 
                   
                     φ 
                     1 
                   
                   + 
                   
                     φ 
                     2 
                   
                   + 
                   
                     φ 
                     3 
                   
                   + 
                   
                     φ 
                     4 
                   
                   + 
                   
                     2 
                     ⁢ 
                     β 
                   
                   - 
                   
                     θ 
                     0 
                   
                   - 
                   
                     2 
                     ⁢ 
                     
                       arctan 
                          
                       [ 
                       
                         tan 
                         ⁢ 
                            
                         
                           
                             ( 
                             
                               
                                 
                                   
                                     φ 
                                     1 
                                     ′ 
                                   
                                   + 
                                     
                                   β 
                                   + 
                                   
                                     φ 
                                     2 
                                     ′ 
                                   
                                   + 
                                   
                                     φ 
                                     3 
                                     ′ 
                                   
                                   + 
                                   
                                     φ 
                                     4 
                                     ′ 
                                   
                                   + 
                                   θ 
                                 
                                 2 
                               
                               - 
                               
                                 a 
                                 ⁢ 
                                 tan 
                                 ⁢ 
                                    
                                 
                                   ( 
                                   
                                     
                                       K 
                                       d 
                                     
                                     ⁢ 
                                     tan 
                                     ⁢ 
                                        
                                     
                                       ( 
                                       
                                         
                                           θ 
                                           0 
                                         
                                         2 
                                       
                                       ) 
                                     
                                   
                                   ) 
                                 
                               
                             
                             ) 
                           
                           / 
                           
                             K 
                             d 
                           
                         
                       
                       ] 
                     
                   
                   + 
                   
                     arctan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           R 
                           ⁢ 
                              
                           
                             sin 
                             ⁡ 
                             ( 
                             
                               β 
                               - 
                               θ 
                             
                             ) 
                           
                         
                         
                           C 
                           - 
                           
                             R 
                             ⁢ 
                                
                             
                               cos 
                               ⁡ 
                               ( 
                               
                                 β 
                                 - 
                                 θ 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     ρ 
                     4 
                   
                   ( 
                   θ 
                   ) 
                 
                 = 
                 
                   
                     
                       C 
                       2 
                     
                     + 
                     
                       R 
                       2 
                     
                     - 
                     
                       2 
                       ⁢ 
                       CR 
                       ⁢ 
                          
                       
                         cos 
                         ⁡ 
                         ( 
                         
                           β 
                           - 
                           θ 
                         
                         ) 
                       
                     
                   
                 
               
               ; 
             
           
         
         OM 6  is taken as a polar axis, a polar diameter corresponding to any position of the curve arc S 67  is OP 6 =ρ 6 (θ), and an included angle between the polar diameter OP 6  and the polar axis OM 6  is a polar angle ε 6 (θ), which satisfies: 
       
       
         
           
             
               
                 
                   
                     ε 
                     6 
                   
                   ( 
                   θ 
                   ) 
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     
                       arctan 
                          
                       [ 
                       ⁠ 
                       
                         tan 
                         ⁢ 
                            
                         
                           ( 
                           
                             
                               
                                 
                                   φ 
                                   1 
                                   ′ 
                                 
                                 + 
                                   
                                 
                                   2 
                                   ⁢ 
                                   β 
                                 
                                 + 
                                 
                                   φ 
                                   2 
                                   ′ 
                                 
                                 + 
                                 
                                   φ 
                                   3 
                                   ′ 
                                 
                                 + 
                                 
                                   φ 
                                   4 
                                   ′ 
                                 
                                 + 
                                 
                                   φ 
                                   4 
                                   ′ 
                                 
                                 + 
                                 
                                   φ 
                                   5 
                                   ′ 
                                 
                                 + 
                                 θ 
                               
                               2 
                             
                             - 
                             
                               a 
                               ⁢ 
                               tan 
                               ⁢ 
                                  
                               
                                 ( 
                                 
                                   
                                     K 
                                     d 
                                   
                                   ⁢ 
                                   tan 
                                   ⁢ 
                                      
                                   
                                     ( 
                                     
                                       
                                         θ 
                                         0 
                                       
                                       2 
                                     
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                           ) 
                         
                         ⁠ 
                         / 
                         
                           K 
                           d 
                         
                       
                       ] 
                     
                   
                   + 
                   
                     θ 
                     0 
                   
                   - 
                   
                     φ 
                     1 
                   
                   - 
                   
                     φ 
                     2 
                   
                   - 
                   
                     φ 
                     3 
                   
                   - 
                   
                     φ 
                     4 
                   
                   - 
                   
                     φ 
                     5 
                   
                   - 
                   
                     2 
                     ⁢ 
                     β 
                   
                   + 
                   
                     arctan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           R 
                           ⁢ 
                              
                           sin 
                           ⁢ 
                           θ 
                         
                         
                           C 
                           - 
                           
                             R 
                             ⁢ 
                                
                             cos 
                             ⁢ 
                             θ 
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     ρ 
                     6 
                   
                   ( 
                   θ 
                   ) 
                 
                 = 
                   
                 
                   
                     
                       C 
                       2 
                     
                     + 
                     
                       R 
                       2 
                     
                     - 
                     
                       2 
                       ⁢ 
                       CR 
                       ⁢ 
                          
                       cos 
                       ⁢ 
                       θ 
                     
                   
                 
               
               ; 
             
           
         
         OM 9  is taken as a polar axis, a polar diameter corresponding to any position of the curve arc S 89  is OP 8 =ρ 8 (θ), and an included angle between the polar diameter OP 8  and the polar axis OM 9  is a polar angle ε 8 (θ), which satisfies: 
       
       
         
           
             
               
                 
                   
                     ε 
                     8 
                   
                   ( 
                   θ 
                   ) 
                 
                 = 
                 
                   
                     φ 
                     1 
                   
                   + 
                   
                     4 
                     ⁢ 
                     β 
                   
                   + 
                   
                     φ 
                     2 
                   
                   + 
                   
                     φ 
                     3 
                   
                   + 
                   
                     φ 
                     4 
                   
                   + 
                   
                     φ 
                     5 
                   
                   + 
                   
                     φ 
                     6 
                   
                   + 
                   
                     φ 
                     7 
                   
                   + 
                   
                     φ 
                     8 
                   
                   - 
                   
                     θ 
                     0 
                   
                   - 
                   
                     
                       2 
                     
                     ⁢ 
                     
                         
                     
                     
                       
                         arctan 
                       
                       
                            
                       
                       
                         [ 
                       
                       
                         tan 
                         ⁢ 
                            
                         
                           ( 
                           
                             
                               
                                 
                                   φ 
                                   1 
                                   ′ 
                                 
                                 + 
                                   
                                 
                                   3 
                                   ⁢ 
                                   β 
                                 
                                 + 
                                 
                                   φ 
                                   2 
                                   ′ 
                                 
                                 + 
                                 
                                   φ 
                                   3 
                                   ′ 
                                 
                                 + 
                                 
                                   φ 
                                   4 
                                   ′ 
                                 
                                 + 
                                 
                                   φ 
                                   4 
                                   ′ 
                                 
                                 + 
                                 
                                   φ 
                                   5 
                                   ′ 
                                 
                                 + 
                                 
                                   φ 
                                   6 
                                   ′ 
                                 
                                 + 
                                 
                                   φ 
                                   7 
                                   ′ 
                                 
                                 + 
                                 
                                   φ 
                                   8 
                                   ′ 
                                 
                                 + 
                                 θ 
                               
                               2 
                             
                             - 
                             
                               a 
                               ⁢ 
                               tan 
                               ⁢ 
                                  
                               
                                 ( 
                                 
                                   
                                     K 
                                     d 
                                   
                                   ⁢ 
                                   tan 
                                   ⁢ 
                                      
                                   
                                     ( 
                                     
                                       
                                         θ 
                                         0 
                                       
                                       2 
                                     
                                     ) 
                                   
                                 
                                 ) 
                               
                             
                           
                           ) 
                         
                         / 
                         
                           K 
                           d 
                         
                       
                       ] 
                     
                   
                   + 
                   
                     arctan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           R 
                           ⁢ 
                              
                           
                             sin 
                             ⁡ 
                             ( 
                             
                               β 
                               - 
                               θ 
                             
                             ) 
                           
                         
                         
                           C 
                           - 
                           
                             R 
                             ⁢ 
                                
                             
                               cos 
                               ⁡ 
                               ( 
                               
                                 β 
                                 - 
                                 θ 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   ρ 
                   8 
                 
                 ( 
                 θ 
                 ) 
               
               = 
               
                 
                   
                     
                       C 
                       2 
                     
                     + 
                     
                       R 
                       2 
                     
                     - 
                     
                       2 
                       ⁢ 
                       CR 
                       ⁢ 
                          
                       
                         cos 
                         ⁡ 
                         ( 
                         
                           β 
                           - 
                           θ 
                         
                         ) 
                       
                     
                   
                 
                 . 
               
             
           
         
       
     
     
       4. The twin-screw extrusion device according to  claim 2 , wherein connection points between every two adjacent curve arcs of the second screw are N 1 , N 2 , N 3 , N 4 , N 5 , N 6 , N 7 , N 8  and N 9 , which respectively correspond to curve arcs S′ 12 , S′ 23 , S′ 34 , S′ 45 , S′ 56 , S′ 67 , S′ 78 , S′ 89  and S′ 91 , and an auxiliary angle is given as θ, 0≤θ≤B;
 O′N 3  is taken as a polar axis, a polar diameter corresponding to any position of the curve arc S′ 23  is OP 2′ =ρ 2′ (θ), and an included angle between the polar diameter OP 2′  and the polar axis ON 3  is a polar angle ε 2′ (θ), which satisfies: 
 
       
         
           
             
               
                 
                   ε 
                   
                     2 
                     ′ 
                   
                 
                 ( 
                 θ 
                 ) 
               
               = 
               
                 
                   φ 
                   1 
                   ′ 
                 
                 + 
                 β 
                 + 
                 
                   φ 
                   2 
                   ′ 
                 
                 - 
                 
                   2 
                   ⁢ 
                   a 
                   ⁢ 
                   
                     tan 
                        
                     [ 
                     ⁠ 
                     
                       
                         
                           
                             K 
                             d 
                           
                           ⁢ 
                           tan 
                           ⁢ 
                              
                           
                             ( 
                             
                               
                                 
                                   φ 
                                   1 
                                 
                                 + 
                                 
                                   φ 
                                   2 
                                 
                                 + 
                                 θ 
                                 - 
                                 
                                   θ 
                                   0 
                                 
                               
                               2 
                             
                             ) 
                           
                         
                         - 
                         
                           2 
                           ⁢ 
                           a 
                           ⁢ 
                           tan 
                           ⁢ 
                           
                                
                           
                           
                             
                               ( 
                             
                             
                               
                                 K 
                                 d 
                               
                               ⁢ 
                               tan 
                               ⁢ 
                                  
                               
                                 ( 
                                 
                                   
                                     θ 
                                     0 
                                   
                                   2 
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           arctan 
                           ⁢ 
                              
                           
                             ( 
                             
                               
                                 R 
                                 ⁢ 
                                    
                                 
                                   sin 
                                   ⁡ 
                                   ( 
                                   
                                     β 
                                     - 
                                     θ 
                                   
                                   ) 
                                 
                               
                               
                                 C 
                                 - 
                                 
                                   R 
                                   ⁢ 
                                      
                                   
                                     cos 
                                     ⁡ 
                                     ( 
                                     
                                       β 
                                       - 
                                       θ 
                                     
                                     ) 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                       ; 
                     
                   
                 
               
             
           
         
         
           
             
               
                 
                   
                     ρ 
                     
                       2 
                       ′ 
                     
                   
                   ( 
                   θ 
                   ) 
                 
                 = 
                 
                   
                     
                       C 
                       2 
                     
                     + 
                     
                       R 
                       2 
                     
                     - 
                     
                       2 
                       ⁢ 
                       CR 
                       ⁢ 
                          
                       
                         cos 
                         ⁡ 
                         ( 
                         
                           β 
                           - 
                           θ 
                         
                         ) 
                       
                     
                   
                 
               
               ; 
             
           
         
         O′N 4  is taken as a polar axis, a polar diameter corresponding to any position of the curve arc S′ 45  is OP 4′ =ρ 4′ (θ), and an included angle between the polar diameter OP 4′  and the polar axis ON 4  is a polar angle ε 4′ (θ), which satisfies: 
       
       
         
           
             
               
                 
                   
                     ε 
                     
                       4 
                       ′ 
                     
                   
                   ( 
                   θ 
                   ) 
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         tan 
                         ⁢ 
                            
                         
                           ( 
                           
                             
                               
                                 φ 
                                 1 
                               
                               + 
                               
                                 φ 
                                 2 
                               
                               + 
                               β 
                               + 
                               
                                 φ 
                                 3 
                               
                               + 
                               θ 
                               - 
                               
                                 θ 
                                 0 
                               
                             
                             2 
                           
                           ) 
                         
                       
                       ) 
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         tan 
                         ⁢ 
                            
                         
                           ( 
                           
                             
                               θ 
                               0 
                             
                             2 
                           
                           ) 
                         
                       
                       ) 
                     
                   
                   - 
                   
                     φ 
                     1 
                     ′ 
                   
                   - 
                   β 
                   - 
                   
                     φ 
                     2 
                     ′ 
                   
                   - 
                   
                     φ 
                     3 
                     ′ 
                   
                   + 
                   
                     arctan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           R 
                           ⁢ 
                              
                           sin 
                           ⁢ 
                           θ 
                         
                         
                           C 
                           - 
                           
                             R 
                             ⁢ 
                                
                             cos 
                             ⁢ 
                             θ 
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     ρ 
                     
                       4 
                       ′ 
                     
                   
                   ( 
                   θ 
                   ) 
                 
                 = 
                 
                   
                     
                       C 
                       2 
                     
                     + 
                     
                       R 
                       2 
                     
                     - 
                     
                       2 
                       ⁢ 
                       CR 
                       ⁢ 
                          
                       cos 
                       ⁢ 
                       θ 
                     
                   
                 
               
               ; 
             
           
         
         O′N 6  is taken as a polar axis, a polar diameter corresponding to any position of the curve arc S′ 67  is OP 6′ =ρ 6′ (θ), and an included angle between the polar diameter OP 6′  and the polar axis ON 6  is a polar angle ε 6′ (θ), which satisfies: 
       
       
         
           
             
               
                 
                   
                     ε 
                     
                       6 
                       ′ 
                     
                   
                   ( 
                   θ 
                   ) 
                 
                 = 
                 
                   
                     
                       
                         φ 
                         1 
                         ′ 
                       
                       ++ 
                     
                     ⁢ 
                     3 
                     ⁢ 
                     β 
                     ⁢ 
                        
                     
                       φ 
                       2 
                       ′ 
                     
                   
                   + 
                   
                     φ 
                     3 
                     ′ 
                   
                   + 
                   
                     φ 
                     4 
                     ′ 
                   
                   + 
                   
                     φ 
                     5 
                     ′ 
                   
                   + 
                   
                     φ 
                     6 
                     ′ 
                   
                   - 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         tan 
                         ⁢ 
                            
                         
                           ( 
                           
                             
                               
                                 φ 
                                 1 
                               
                               + 
                               
                                 2 
                                 ⁢ 
                                 β 
                               
                               + 
                               
                                 φ 
                                 2 
                               
                               + 
                               
                                 φ 
                                 3 
                               
                               + 
                               
                                 φ 
                                 4 
                               
                               + 
                               
                                 φ 
                                 5 
                               
                               + 
                               
                                 φ 
                                 6 
                               
                               + 
                               θ 
                               - 
                               
                                 θ 
                                 0 
                               
                             
                             2 
                           
                           ) 
                         
                       
                       ) 
                     
                   
                   - 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         tan 
                         ⁢ 
                            
                         
                           ( 
                           
                             
                               θ 
                               0 
                             
                             2 
                           
                           ) 
                         
                       
                       ) 
                     
                   
                   + 
                   
                     arctan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           R 
                           ⁢ 
                              
                           
                             sin 
                             ⁡ 
                             ( 
                             
                               β 
                               - 
                               θ 
                             
                             ) 
                           
                         
                         
                           C 
                           - 
                           
                             R 
                             ⁢ 
                                
                             
                               cos 
                               ⁡ 
                               ( 
                               
                                 β 
                                 - 
                                 θ 
                               
                               ) 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   
                     p 
                     
                       6 
                       ′ 
                     
                   
                   ( 
                   θ 
                   ) 
                 
                 = 
                 
                   
                     
                       C 
                       2 
                     
                     + 
                     
                       R 
                       2 
                     
                     - 
                     
                       2 
                       ⁢ 
                       CR 
                       ⁢ 
                          
                       
                         cos 
                         ⁡ 
                         ( 
                         
                           β 
                           - 
                           θ 
                         
                         ) 
                       
                     
                   
                 
               
               ; 
             
           
         
         O′N 8  is taken as a polar axis, a polar diameter corresponding to any position of the curve arc S′ 89  is OP 8′ =ρ 8′ (θ), and an included angle between the polar diameter OP 8′  and the polar axis ON 7  is a polar angle ε 8′ (θ), which satisfies: 
       
       
         
           
             
               
                 
                   
                     ε 
                     
                       8 
                       ′ 
                     
                   
                   ( 
                   θ 
                   ) 
                 
                 = 
                 ⁠ 
                 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         tan 
                         ⁢ 
                            
                         
                           ( 
                           
                             
                               
                                 φ 
                                 1 
                               
                               + 
                               
                                 3 
                                 ⁢ 
                                 β 
                               
                               + 
                               
                                 φ 
                                 2 
                               
                               + 
                               
                                 φ 
                                 3 
                               
                               + 
                               
                                 φ 
                                 4 
                               
                               + 
                               
                                 φ 
                                 5 
                               
                               + 
                               
                                 φ 
                                 6 
                               
                               + 
                               
                                 φ 
                                 7 
                               
                               + 
                               θ 
                               - 
                               
                                 θ 
                                 0 
                               
                             
                             2 
                           
                           ) 
                         
                       
                       ) 
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     a 
                     ⁢ 
                     tan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           K 
                           d 
                         
                         ⁢ 
                         tan 
                         ⁢ 
                            
                         
                           ( 
                           
                             
                               θ 
                               0 
                             
                             2 
                           
                           ) 
                         
                       
                       ) 
                     
                   
                   - 
                   
                     φ 
                     1 
                     ′ 
                   
                   - 
                   
                     φ 
                     2 
                     ′ 
                   
                   - 
                   
                     φ 
                     3 
                     ′ 
                   
                   - 
                   
                     φ 
                     4 
                     ′ 
                   
                   - 
                   
                     φ 
                     5 
                     ′ 
                   
                   - 
                   
                     φ 
                     6 
                     ′ 
                   
                   - 
                   
                     φ 
                     7 
                     ′ 
                   
                   - 
                   
                     3 
                     ⁢ 
                     β 
                   
                   + 
                   
                     arctan 
                     ⁢ 
                        
                     
                       ( 
                       
                         
                           R 
                           ⁢ 
                              
                           sin 
                           ⁢ 
                           θ 
                         
                         
                           C 
                           - 
                           
                             R 
                             ⁢ 
                                
                             cos 
                             ⁢ 
                             θ 
                           
                         
                       
                       ) 
                     
                   
                 
               
               ; 
             
           
         
         
           
             
               
                 
                   p 
                   
                     8 
                     ′ 
                   
                 
                 ( 
                 θ 
                 ) 
               
               = 
               
                 
                   
                     
                       C 
                       2 
                     
                     + 
                     
                       R 
                       2 
                     
                     - 
                     
                       2 
                       ⁢ 
                       CR 
                       ⁢ 
                          
                       cos 
                       ⁢ 
                       θ 
                     
                   
                 
                 . 
               
             
           
         
       
     
     
       5. The twin-screw extrusion device according to  claim 1 , wherein, along an axial direction of the first screw, the barrel is sequentially provided with a conveying section, a melting section, an exhaust section and a mixing extrusion section, the conveying section is provided with a feed inlet, the exhaust section is provided with an exhaust outlet, and the mixing extrusion section is provided with a discharge outlet. 
     
     
       6. The twin-screw extrusion device according to  claim 1 , wherein both an outer diameter of the first screw and an outer diameter of the second screw are tangent to an inner wall of the barrel.

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